The graph shows us that the slope of f(x) is -2. Now we gotta find the slope of g(x) to compare it to that of f(x). The equation of g(x) is in slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept), so the slope is given to us for that one as well: it's -6. A line with a slope of -6 will be steeper than a line with a slope of -3, therefore the answer is B - the slope of f(x) is less than the slope of g(x).
Hope this helps.
<span>Constraints (in slope-intercept form)
x≥0,
y≥0,
y≤1/3x+3,
y</span>≤ 5 - x
The vertices are the points of intersection between the constraints, or the outer bounds of the area that agrees with the constraints.
We know that x≥0 and y≥0, so there is one vertex at (0,0)
We find the other vertex on the y-axis, plug in 0 for x in the function:
y <span>≤ 1/3x+3
y </span><span>≤1/3(0)+3
y = 3.
There is another vertex at (0,3)
Find where the 2 inequalities intersect by setting them equal to each other
(1/3x+3) = 5-x Simplify Simplify Simplify
x = 3/2
Plugging in 3/2 into y = 5-x: 10/2 - 3/2 = 7/2
y=7/2
There is another vertex at (3/2, 7/2)
There is a final vertex where the line y=5-x crosses the x axis:
0 = 5 -x , x = 5
The final vertex is at point (5, 0)
Therefore, the vertices are:
(0,0), (0,3), (3/2, 7/2), (5, 0)
We want to maximize C = 6x - 4y.
Of all the vertices, we want the one with the largest x and smallest y. We might have to plug in a few to see which gives the greatest C value, but in this case, it's not necessary.
The point (5,0) has the largest x value of all vertices and lowest y value.
Maximum of the function:
C = 6(5) - 4(0)
C = 30</span>
Answer: 60
Step-by-step explanation:
As JH=22 and JK=82, this means HK=60.
Hi there!
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I believe your answer is:
(-3, -1) and (1, 3)
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Here’s why:
- I have graphed the two equations given on a graphing program.
- When graphed, they pass at points (-3, -1) and (1,3). Therefore, they are the solutions to the system.
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See the graph attached.
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Hope this helps you. I apologize if it’s incorrect.
